arXiv subjects

Huiming Yin

Publications and source records attributed to Huiming Yin.

5 recordsLinked to original sources

arXiv2026

Bimaterial Eshelby's inclusion problem for polyhedra

This paper presents the closed-form Eshelby's tensor for an arbitrarily oriented polyhedral inclusion in a bimaterial domain under general uniform eigenstrain. Existing bimaterial solutions are mainly restricted to special inclusion shapes or dilatational eigenstrains, because the bimaterial Green's function contains two Boussinesq's displacement potentials in addition to the harmonic and biharmonic potentials in Kelvin's solution. This paper derives the missing domain integrals of the two Boussinesq's potentials by reducing the volume integrals to surface and elementary line integrals. The formulae provide the complete elastic and thermoelastic bimaterial Eshelby's tensors, which are verified against analytical solutions for spherical and cuboidal inclusions parallel to the bimaterial interface, and finite element results of an inclined cuboid. Singularity analysis demonstrates that the interface-related contribution remains regular when the inclusion is separated from the bimaterial interface, while additional logarithmic singularities arise when an edge or vertex touches the interface without increasing the dominant singularity order.

math-ph↗

arXiv2026

Nonlocal thermal Willis coupling in laminated conductors

Building on Willis' homogenization framework, recent work has revealed that heterogeneous conductors exhibit macroscopic thermal bianisotropy, in which the macroscopic heat flux and entropy are nonlocally coupled to both temperature and temperature gradient. Existing numerical examples, however, are limited to the subwavelength regime. Here, we provide the first explicit demonstration of this spatial nonlocality by computing the effective kernels of a periodic laminate using three independent homogenization methods. The three approaches yield consistent nonlocal cross-coupling terms, clarifying the roles of spatial asymmetry and averaging choice. We also calculate the corresponding thermal impedance and show that it is direction-dependent, highlighting a physical signature of thermal bianisotropy relevant to thermal metamaterials.

math-ph↗

arXiv2025

Singularities at the vertex of connected angular inhomogeneities under thermal and elastic loading

This paper investigates the singularities at the vertex of multiply connected angular inhomogeneities for heat conduction and elastic deformation. With the aid of Eshelby's equivalent inclusion method (EIM), each inhomogeneity is simulated as an equivalent inclusion, exhibiting the same material properties as the matrix but containing a continuously distributed eigen-field with potential singularities at the vertices and edge lines. Specifically, the eigen-temperature-gradient (ETG) and eigenstrain are utilized to simulate material mismatch of thermal conductivity and stiffness, respectively. Using the separation of variables, the eigen-fields can be formulated in terms of distance to vertices and opening angles, and disturbed thermal/elastic fields are evaluated by domain integrals of Green's function multiplied by eigen-fields, which form Fredholm's integral equation of the second kind. The boundary value problem is reduced to solve for eigenvalues, which are used to determine the order of singularity. The present solution is versatile - by placing two identical inhomogeneities together, it recovers the classic solutions for a single wedge in a bimaterial media or infinite domain. The general and analytical formulae take full consideration of interactions of multiple inhomogeneities and reveal the effects of opening angles and material properties on the thermal and elastic singularities.

math-ph↗

arXiv2025

Transient thermal analysis of a bi-layered composites with the dual-reciprocity inclusion-based boundary element method

This paper proposes a single-domain dual-reciprocity inclusion-based boundary element method (DR-iBEM) for a three-dimensional fully bonded bi-layered composite embedded with ellipsoidal inhomogeneities under transient/harmonic thermal loads. The heat equation is interpreted as a static one containing time- and frequency-dependent nonhomogeneous source terms, which is similar to eigen-fields but is transformed into a boundary integral by the dual-reciprocity method. Using the steady-state bimaterial Green's function, boundary integral equations are proposed to take into account continuity conditions of temperature and heat flux, which avoids setting up any continuity equations at the bimaterial interface. Eigen-temperature-gradients and eigen-heat-source are introduced to simulate the material mismatch in thermal conductivity and heat capacity, respectively. The DR-iBEM algorithm is particularly suitable for investigating the transient and harmonic thermal behaviors of bi-layered composites and is verified by the finite element method (FEM). Numerical comparison with the FEM demonstrates its robustness and accuracy. The method has been applied to a functionally graded material as a bimaterial with graded particle distributions, where particle size and gradation effects are evaluated.

math.NA↗

arXiv2025

Generalized Eshelby's inclusion and inhomogeneity problems for transient heat transfer

Eshelby's inclusion problems have been generalized to arbitrary shape of polygonal, polyhedral, and ellipsoidal inclusions embedded in an infinite isotropic domain under transient heat transfer, and Eshelby's tensors have been analytically derived to evaluate disturbed thermal fields caused by inclusions with a polynomial-form eigen-field. Transformed coordinates are applied to arbitrarily shaped inclusions for domain integrals of transient fundamental solutions. This formulation is for general transient heat transfer, and it can recover classic Eshelby's tensor for the ellipsoidal subdomain with explicit expression for the spherical domain in the steady state, Michelitsch's solution in the harmonic state, and recent solution in the transient state. The formulae for a polyhedral inclusion is verified by comparison to closed-form solutions of a spherical inclusion when the sphere is divided into many polyhedrons. The discontinuity of domain integrals for Eshelby's tensor are investigated the temporal effects are elaborated. The generalized formulation for Eshelby's problems enables the simulation and modeling of particulate composites containing inhomogeneities of various shapes for steady-state, harmonic and transient heat transfer in both two- and three-dimensional space through the equivalent inclusion method.

math-ph↗